Question

The parent function, (f(x) = 5x), has been vertically compressed by a factor of one-half, shifted to the right three units, and down two units. Choose the correct function to represent the transformation.

a) (g(x)=5^1/2x-3-2)
b) (g(x)=(1/2)⁵x+3-2)
c) (g(x)=5^1/2x+3-2)
d) (g(x)=(1/2)⁵x-3-2)

Answer 1

The correct function after applying the described transformations to the parent function f(x) = 5x is g(x) = (1/2) * 5 * (x - 3) - 2.

Step-by-step explanation:

The student is asked about the transformation of a parent function after it has been vertically compressed, shifted to the right, and shifted downwards. Starting with the parent function f(x) = 5x, a vertical compression by a factor of one-half would multiply the function by 1/2, shifting to the right by three units would replace x with (x - 3), and shifting down by two units would subtract 2 from the entire function. Therefore, the function would be g(x) = (1/2) * 5 * (x - 3) - 2.